1. Introduction to Interferometric Synthetic Aperture Radar - InSAR
There are several applications to InSAR. We shall focus on the mapping of surface deformation.
Principals of InSAR (based largely on: epsilon.nought.de/tutorials/insar_tmr/img0.htm)
Case studies and applications

2. Dr Change in LOS Df Second Acquisition (Slave)
First Acquisition (Master)
5.56 mm
Master
Slave Df r1 r2
Dr
Change in LOS

3. The satellite orbit was fixed.
If:
Earth was flat.
The satellite orbit was fixed.
No atmosphere.
Then:
Things were simple, and the calculation of ground deformation would have been indeed an easy task.
In practice, however, in order to obtain the deformation field, it is necessary to perform quite a few corrections.

4. Viewing Position
Spherical Earth
Topography
Atmosphere
Deformation

5. SAR is an active sensor
Unlike passive sensors, the SAR transmits a signal and measures the reflected wave. So the SAR can “see” day-and-night.
The signal wave length was selected such that its absorption by atmospheric molecules is minimal.
ERS

6. SAR geometry ERS1/2 azimuth range
Launch date: ERS1 July 1991 ERS2 April 1995
Altitude: km
Incidence angle: 23 degrees
Period: minutes
Repeat time: 35 days

7. Ascending and descending
Orbit geometry
Polar (almost) orbit
Ascending and descending
Ground tracks
Ascending
track
Descending
track

8. The (SAR) data
The SAR records the amplitude and the phase of the returned signal
amplitude
phase
Mt. Etna
Image from
Note that while the amplitude image shows recognizable topographic pattern, the phase image looks random.

9. The phase
The phase is mostly due to the propagation delay, but also due to coherent sum of contributions from scatters within the resolution element.
Figure from Rosen et al., 2000

10. The phase
The phase is proportional to the two-way travel distance divided by the transmitted wavelength.
Due to the periodic nature of the signal, travel distances that differ by an integer multiple of the wave length introduce exactly the same phase difference.

11. InSAR geometry The baseline, B, is the orbit separation vector.
Baselines should be less than 200 meters, and the shorter the better!

12. amplitude coregistration
InSAR processing:
amplitude coregistration
The two images, i.e. the “slave” and the “master”, do not overlap. So we need to figure out which group of pixels in the “slave” corresponds to which group of pixels in the “master”. This is done through cross-correlating sub-areas in the two images.
This step requires a huge number of operations, and is by far the most time consuming step in the process.
Image from

13. - = InSAR processing: phase interferogram
Calculate phase interferogram, i.e. subtract the phase of of the “slave” from that of the “master”.
phase “master”
phase “slave”
phase interferogram - =
Note that while both the master and slave appear random, the interferogram does not.

14. - = InSAR processing: flat-earth removal
Next, we need to remove the phase interferogram that would result from a flat-earth. - =
After removing the flat-earth effect we are left with an interferogram that contains topography+deformation between the two acquisitions and atmospheric effect.

15. Remove topographic phase
InSAR processing:
Remove topographic phase
Height of ambiguity: the amount of height change that leads to a 2 change in interferometric change:

16. Remove topographic phase (cont.)
InSAR processing:
Remove topographic phase (cont.)
The longer the baseline, the smaller the topographic height needed to produce a fringe of phase change (or, the longer the baseline is the stronger the topographic imprint).
Image from

17. InSAR processing: unwrapping
The interferogram is a map of an ambiguous phase offset between - and +. In order to recover the absolute unambiguous phase offset, one needs to unwrap the data.
Phase unwrapping is a tricky business, here’s one algorithm:
Image from

18. While the wrapped phase looks like this:
The unwrapped phase looks like this:
* Note that in this specific example the topographic effect has not been removed, thus the unwrapped phase map correspond mainly to topographic height.

19. InSAR processing: geocoding
This final step amounts to mapping the phase from satellite to geographic coordinates.
azimuth
latitude
range
longitude
Figure from:

20. The seismic cycle:
Figure from: Wright, 2002.

21. Seismic displacement:
The utilization of SAR data to map surface deformation started with the ground-breaking study of the 1992 Landers earthquake in California [Massonnet et al., 1993].
Massonnet, D., M. Rossi, C. Carmona, F. Adragna, G. Peltzer, K. Feigl, and T. Rabaute, The displacement field of the Landers earthquake mapped by radar interferometry, Nature, 364, , 1993.

22. Seismic displacement (cont.):
It is hard to unwrap the interferogram, if the deformation is discontinuous. In such cases, it is convenient to present the results in wrapped form.
Yellow-red-blue : target moved a way from the satellite.
Red-yellow-blue : target moved towards the satelite.
Figure from:

23. ML=4.6, Depth= 10 km 10/10/2003 – 11/06/2004 Earthquakes E Meters
-0.16
0.16
Meters
(א)
(ב)
Residual Model Signal E
Lat
Lon
L (km)
Upper Depth (km)
Lower Depth (km)
Strike
Dip
Rake
Slip (m) Mw
RMS (m)
31.47
59.40
4.30
3.893
4.489
115.55
64.58
58.52
0.703
4.4
1.1*10-3
ניתן להבחין באות שמקורו ברעידת אדמה בעלת מגניטודה 4.6 שהתרחשה בתאריך 21/11/2003. מוקד הרעידה מרוחק כ- 24 ק"מ צפונית לאזור האות שמופיע על גבי האינטרפרוגרמה. כדי לוודא שהאינטרפרוגרמה אכן מראה רעידת אדמה בדקנו אינטרפרוגרמות של אותו אזור בזמנים שונים, שאינם כוללים את הרעידה. ניתן לראות כי האות אינו חוזר על עצמו באינטרפרוגרמות האחרות, אינו עוקב אחרי טופוגרפיה ומתפרש על אזור קטן מבחינה מרחבית. יתר על כן, פתרון המודל מראה התאמה טובה לאינטרפרוגרמה. גם במקרה זה נמצאה התאמה טובה בין המומנט הסיסמי והמומנט הגיאודטי (המחושב על ידי המודל). בגלל גודלה הקטן, לא קיים פתרון מוקד לרעידה זו הניתן להשוואה עם המודל.

24. Seismic displacement (cont.):
It turned out that the crust is an elastic half-space!
Magnitude 5.6 from Western Iran. Processed and calculated by Maytal Sade

25. Seismic displacement (cont.):
The 1999 Izmit earthquake in Turkey [Wright et al., 2001]

26. Seismic displacement (cont.):
The 1999 Izmit earthquake in Turkey [Wright et al., 2001]
Modeling the data helps to:
Constrain the rupture geometry and co-seismic slip distribution.
Identify triggered slip.

27. Seismic displacement (cont.):
The 1999 Izmit earthquake in Turkey [Wright et al., 2001]

28. Seismic displacement (cont.):
The displacement field projected onto a map view may be obtained by using both the ascending and the descending tracks. In order to go beyond the 2D displacement field, an additional information should be incorporated - the azimuth offset.
The 3-D displacement field in the area of 1999 Hector Mine in California (Fialko et al., 2001):
The 3 equations:
The 3 unknowns:

29. Inter-seismic displacement:
Obviously, resolving co-seismic (large) deformation is easier than resolving inter-seismic (small) deformation. The signal to noise ratio may be amplified by stacking multiple interferograms (the more the better).
Application of the stacking approach to NAF (Wright et al., 2001):
Because inter-seismic strain accumulates steadily with time, the contribution of each pair is scaled proportionally to the interval between acquisitions.

30. Inter-seismic displacement (cont.):
Figure from Wright et al., [2001, GRL]
A recipe for reducing atmospheric contribution:
It is useful to form interferogram chains in such a way that each date is used as a master the same number of times it is used as a slave. The atmospheric effect of these acquisitions is exactly canceled out, and we are left only with the atmospheric contribution from the start and the end of the chain (see Holley, 2004, M.Sc. thesis, Oxford).

31. Earthquake location:
Locating small-moderate quakes in southern Iran (Lohman and Simons, 2005):
Figure from Pritchard, 2006, Physics Today